Knowledge Organiser: Probability Problems
Part of Probability Problems · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Probability Problems within Probability Problems for GCSE Mathematics. Revise Probability Problems in Probability for GCSE Mathematics with 12 exam-style questions and 5 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 6 of 6 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 6 of 6
Practice
12 questions
Recall
5 flashcards
Knowledge Organiser: Probability Problems
Key Terms
- At least one: Use P(at least one) = 1 − P(none)
- Exactly n: Identify all paths giving exactly n successes and add them
- Given that: Signals conditional probability — reduce the sample space
- Without replacement: Each draw reduces the total; probabilities change
- Independent scenario: Two separate experiments — multiply their probabilities
- Complement method: P(event) = 1 − P(opposite event)
Must-Know Facts
- Read the question carefully — identify what you are asked to find
- "At least one" is almost always easier via the complement: 1 − P(none)
- Multi-stage problems: draw a tree diagram and multiply along paths
- Overlapping groups: use a Venn diagram
- Survey data with two variables: use a two-way table
- For separate, independent experiments: multiply their individual probabilities
- Always check that a final probability lies between 0 and 1
Key Methods
- P(at least one) = 1 − P(none at all)
- P(A and B, independent) = P(A) × P(B)
- P(A and B, dependent) = P(A) × P(B|A)
- Tree diagram: multiply along paths, add across matching paths
- Venn diagram: fill intersection first, then "only" regions, then "neither"
- Expected frequency = probability × number of trials
Key Formulas
- P(at least one) = 1 − P(none)
- P(A and B, independent) = P(A) × P(B)
- P(A and B, dependent) = P(A) × P(B|A)
- Expected frequency = P(event) × number of trials
Common Mistakes
- "At least one" shortcut: P(at least one) = 1 − P(none) is much quicker than listing all cases where one or more occur
- Without replacement changes probabilities: After removing one item, the denominator decreases for the second draw
- Choosing wrong method: Identify whether events are independent or dependent before choosing the multiplication rule
- Adding when you should multiply: "A and B both happen" → multiply; "A or B happens" → add (and subtract overlap)
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Read this section alongside the surrounding pages in Probability Problems. That gives you the full topic sequence instead of a single isolated revision point.
Practice Questions for Probability Problems
In an experiment, a coin is flipped 50 times and lands heads 32 times. What is the relative frequency of heads?
A student flips a coin 10 times and gets 7 heads. They say the probability of heads is 7/10. Explain why carrying out more trials would give a better estimate of the probability.
Quick Recall Flashcards
12 questions on Probability Problems — practise free
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